Math Problem Statement

Researchers in a 2015 study sought to estimate the effectiveness of the seasonal influenza vaccine in preventing acute respiratory infection (ARI). They wish to construct a 95% z-confidence interval for the proportion of patients with ARI symptoms who would test positive for influenza. Calculate the lower and upper bounds of this confidence interval.

Solution

To solve the problem in the image, let's calculate the 95% confidence interval for the proportion of patients with ARI symptoms who would test positive for influenza:

Formula for a confidence interval for proportion:

CI=p^±Zp^(1p^)nCI = \hat{p} \pm Z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}

Where:

  • p^\hat{p}: sample proportion (number of successes / total sample size)
  • ZZ: critical value for the desired confidence level (for 95%, Z=1.96Z = 1.96)
  • nn: sample size

Let me extract the data from the uploaded image. Could you provide the specific data (e.g., the number of positive cases and total sample size)? If you are unable to provide it, I can guide you to calculate the answer based on the visible information.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Proportions

Formulas

CI = p̂ ± Z * sqrt(p̂(1-p̂)/n)

Theorems

Central Limit Theorem

Suitable Grade Level

College level or advanced high school (Grades 11-12)